Prove that the following relations are equivalenece relations and identify equivalence classes: 1. On R, x y, if x y is an integer. 2. On R 2 ,(x1, y1) (x2, y2) if x1 = x2. 3. On R 2 {(0, 0)},(x1, y1) (x2, y2) if there exists a R, a 6= 0, such that x1 = ax2 and y1 = ay2.

93 Views

Prove that the following relations are equivalenece relations and identify equivalence classes: 1. On R, x y, if x y is an integer. 2. On R 2 ,(x1, y1) (x2, y2) if x1 = x2. 3. On R 2 {(0, 0)},(x1, y1) (x2, y2) if there exists a R, a 6= 0, such that x1 = ax2 and y1 = ay2.

Akash Girde 7th Nov, 2020

Answer

Answer Later

Report

Answer (1)

Anuj More 7th Nov, 2020

Dear Akash,

What you are asking is to prove a mathematical statement. Kindly note this is not possible on this platform as we are limited by our answering ways. You may search this query on internet and you may find various portals which may help you understand your query.

Hope this helps. Thanks.

Like Share

Related Questions

For x, y R define x y to mean that x y Z. 1. Prove that is an equivalence relation on R. 2. List three real numbers x such that x 2.

108 Views

Problem 1.4. For x,y ∈ R def i ne x ∼ y to mean that x − y ∈ Z. 1)Prove that ∼ is an equivalence relation on R. 2)List three real numbers x such that x ∼ √2.

125 Views

For x, y R define x y to mean that |x| = |y|. Prove that is an equivalence relation in R. Describe [0], [5], and [5].

141 Views

For x,y ∈ R def i ne x ∼ y to mean that |x| = |y|. Prove that ∼ is an equivalence relation in R. Describe [0],[5], and [−5].

368 Views

For a, b belongs to R define xRy to mean that x-y belongs to Z. (1) Prove that Relation is an equivalence relation on R. (2) List three real numbers x such that x related to square root 2

89 Views

Applications for Admissions are open.

Amity University, Noida Law A...

Apply

700+ Campus placements at top national and global law firms, corporates and judiciaries

Amity University, Noida BBA A...

Apply

Ranked amongst top 3% universities globally (QS Rankings)

VIT Bhopal University | M.Tec...

Apply

M.Tech admissions open @ VIT Bhopal University | Highest CTC 52 LPA | Apply now

Amity University | M.Tech Adm...

Apply

Ranked amongst top 3% universities globally (QS Rankings).

Graphic Era (Deemed to be Uni...

Apply

NAAC A+ Grade | Among top 100 universities of India (NIRF 2024) | 40 crore+ scholarships distributed

Great Lakes PGPM & PGDM Admis...

Apply

Admissions Open | Globally Recognized by AACSB (US) & AMBA (UK) | 17.3 LPA Avg. CTC for PGPM 2024

View All Application Forms

Trending Articles/News

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students

30,000+ Colleges

500+ Exams

1500+ E-books